#252 ⟨a, b | aaba=bab⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic group

Properties

Rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
#RuleProof
1. a2ba ⇒ bab [1]
2. a2b2ab ⇒ (ba)3 [2]
# ab:aaba=bab ba
aaba=bab
aabbab=bababa

Other submonoids of same group

11 unique, 55 total

Σ#PresentationDescriptionRelated
6104⟨a, b | aaba=bb⟩Infinite cancellative non-commutative monoid
7145⟨a, b | aababba=1⟩Infinite non-Abelian group22 iso, 22 anti-iso
7193⟨a, b | ababba=b⟩Infinite cancellative non-commutative monoid
9842⟨a, b | abaababa=b⟩Infinite cancellative non-commutative monoid
91126⟨a, b | ababba=bab⟩Infinite cancellative non-commutative monoid
91273⟨a, b | abbba=babb⟩Infinite cancellative non-commutative monoid
102633⟨a, b | abbbba=babb⟩Infinite cancellative non-commutative monoid
113716⟨a, b | abaaabaaba=b⟩Infinite cancellative non-commutative monoid
114876⟨a, b | abbabbba=bab⟩Infinite cancellative non-commutative monoid
115415⟨a, b | abbbbba=babb⟩Infinite cancellative non-commutative monoid
115898⟨a, b | ababba=babab⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

7 unique, 7 total

Σ#PresentationDescriptionRelated
687⟨a, b | aabba=b⟩Infinite cancellative non-commutative monoid
7179⟨a, b | aababa=b⟩Infinite cancellative non-commutative monoid
8374⟨a, b | aabaaba=b⟩Infinite cancellative non-commutative monoid
8586⟨a, b | baab=aaba⟩Infinite cancellative non-commutative monoid
9792⟨a, b | aabaaaba=b⟩Infinite cancellative non-commutative monoid
101666⟨a, b | aabaaaaba=b⟩Infinite cancellative non-commutative monoid
113536⟨a, b | aabaaaaaba=b⟩Infinite cancellative non-commutative monoid